MCQ
Choose the correct answers:
If [x]2 - 5[x] + 6 = 0, where [.] denote the greatest integer function, then.
If [x]2 - 5[x] + 6 = 0, where [.] denote the greatest integer function, then.
- Ax ∈ [3, 4]
- Bx ∈ (2, 3]
- Cx ∈ [2, 3]
- Dx ∈ [2, 4)
Solution:
We have [x]2 - 5[x] + 6 = 0
⇒ [x]2 - 3[x] 2[x] + 6 = 0
⇒ [x]([x] - 3) -2([x] - 3) = 0
⇒ ([x] - 3)([x] - 2) = 0 ⇒ [x] = 2, 3
So, x ∈ [2, 3]
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If the coefficient of x in $\Big(\text{x}^{2}+\frac{\lambda}{\text{x}}\Big)^{5}$ is 270, then $\lambda=$